Multiscale instabilities in soft heterogeneous dielectric elastomers

by S. Rudykh, K. Bhattacharya and G. deBotton, Proc. R. Soc. A 470: 20130618.
The development of instabilities in soft heterogeneous dielectric elastomers is investigated. Motivated by experiments and possible applications, we use in our analysis the physically relevant referential electric field instead of electric displacement. In terms of this variable, a closed form solution is derived for the class of layered neo-Hookean dielectrics. A criterion for the onset of electromechanical multiscale instabilities for the layered composites with anisotropic phases is formulated. A general condition for the onset of the macroscopic instability in soft multiphase dielectrics is introduced. In the example of the layered dielectrics, the essential influence of the microstructure on the onset of instabilities is revealed. We found that:
(i) macroscopic instabilities dominate at moderate volume fractions of the stiffer phase,
(ii) interface instabilities appear at small volume fractions of the stiffer phase and
(iii) instabilities of a finite scale, comparable to the microstructure size, occur at large
volume fractions of the stiffer phase.
The latest new type of instabilities does not appear in the purely mechanical case and dominates in the region of large volume fractions of the stiff phase.